相关论文: The All-or-Nothing Phenomenon in Sparse Tensor PCA

Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general…

Coherent perfect absorption (CPA) is an interference process associated with the zeros of the scattering matrix that enables light-with-light interactions in linear systems, of interest for optical computing, data processing and sensing.…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

Single-cell RNA-seq provides detailed molecular snapshots of individual cells but is notoriously noisy. Variability stems from biological differences and technical factors, such as amplification bias and limited RNA capture efficiency,…

We report the experimental realization of acoustic coherent perfect absorption (CPA) of four symmetric scatterers of very different structures. The only conditions necessary for these scatterers to exhibit CPA are that both the reflection…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group…

We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…

We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…

We consider the problem of detecting the presence of a signal in a rank-one spiked Wigner model. For general non-Gaussian noise, assuming that the signal is drawn from the Rademacher prior, we prove that the log likelihood ratio (LR) of the…

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

We establish the convergence rates and asymptotic distributions of the common break change-point estimators, obtained by least squares and maximum likelihood in panel data models and compare their asymptotic variances. Our model assumptions…

We propose an efficient algorithm for tensor PCA based on counting a specific family of weighted hypergraphs. For the order-$p$ tensor PCA problem where $p \geq 3$ is a fixed integer, we show that when the signal-to-noise ratio is $\lambda…

This paper addresses the estimation of signals with sublinear sparsity sent over the additive white Gaussian noise channel. This fundamental problem arises in designing denoisers used in message-passing algorithms for sublinear sparsity.…

The null hypothesis in Pulsar Timing Array (PTA) analyses includes assumptions about ensemble properties of pulsar time-correlated noise. These properties are encoded in prior probabilities for the amplitude and the spectral index of the…

In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Although federated learning has gained prominence as a privacy-preserving framework tailored for distributed Internet of Things (IoT) environments, current federated principal component analysis (PCA) methods lack integration of sparsity, a…

We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between…